Egalitarian-in-deviation rules relative to a reference system for resolving conflicting claims problems

Abstract We study claims problems in which agents may also have reference points. We show first that many classical rules satisfy an egalitarian property in this setting; namely, the differences between each agents’ payoff and the corresponding reference value are as equal as possible. We also introduce a broad class of rules that satisfy a generalized condition, dubbed egalitarian-in-deviation relative to a reference system. For each problem, the system proposes a reference vector which is a function of the claims. We show that these rules allocate the nearest efficient point to the reference vector. Our findings generalize previous results in the literature, such as the one stating that the CEA rule minimizes the squared distance to the equal division point. Concede-and-divide, a focal rule to solve two-agent claims problems, does not satisfy the egalitarian-in-deviation condition relative to any reference system. But, under certain conditions, it can be reinterpreted as the limit of a weighted egalitarian-in-deviation rule. Finally, we explore the behavior of egalitarian-in-deviation rules with respect to the important notions of consistency and duality.